In the previous sections we have dealt with the collection of
data and the estimation of the parameters of growth and total
mortality. These are essential steps in most assessment work, but
they do not in themselves provide assessments in the sense of
statements about the state of the fish stocks, the impact on them of
exploitation, and the effects of alternative policies for the future
development or management of the fishery. This statement of the
nature of assessment suggests that the process can be divided into
three stages; first, the simple determination that fishing is (or is
not) having an impact on the stock, with some indication of the
extent of that impact; second, putting this qualitative statement
into quantitative terms, such as the determination of the relation
between yield-per-recruit and fishing effort, which will lead to the
formulation of long-term strategic advice; and third, the provision
of tactical advice, for example on the level of the Total Allowable
Catch for next year.

The first stage is a matter of detecting some signal imposed on
the stock by changing amounts of fishing. This can be of two kinds
- changes in abundance, or changes in composition. The first may be
detected in changed cpue in the commercial fishery, or less usually
from surveys of one kind or another. In either case information on
length is not relevant. The second kind of signal will arise because
increased fishing will cause increased mortality, and hence result
in relatively fewer old fish, and also (unless the fish do not grow
much after recruiting to the fishery) fewer big fish.

In most fisheries, therefore, a simple sign of heavy fishing is
a change in the size of fish. Figures 4.1 and 4.2 show the changes
in the size composition of catches of plaice in the North Sea, and
of hake to the westward of the British Isles as a result of the
almost complete cessation of fishing during the two world wars. These
are typical of the effects, though perhaps showing them more clearly
than most data sets, because of the big changes in the amount of
fishing over a short period. They are also typical in that there are
two quite distinct changes. As expected, the post-war length-frequencies
show a more extended right-hand limb, indicating a better
survival. There is also a change in the left-hand limb, with the very
small fish being much scarcer in the catches than in the pre-war
periods of heavy fishing.

Figure 4.1 Age-composition (upper two fiqures) and length-composition
of North Sea plaice (lower figure)
sampled just before and just after the first
world war (data from Bannister, 1977). Note that
there is a shift to the right after the war and
not just an increase in older and bigger fish

Figure 4.2 Length-composition of hake landed by English
trawlers in 1946, just after the second world
war, and in 1955 after a period of renewed heavy
fishing. The difference in slope was taken as an
index of the increase in total mortality (data
from Gulland, 1956)

The change among the smaller fish is not easily explained by
changes in mortality alone, and there must be some change in the
pattern of entry to the catches, or perhaps more accurately the
landings. The hake data, and probably the plaice data, are of
commercial landings, and the relative shortage of small fish might,
in part, reflect increased discarding of small fish when bigger fish
are abundant. It may also reflect a shift in fishing grounds towards
the areas where larger fish are abundant, and which were not
attractive during periods of heavy fishing. Whatever the precise
explanation, the result has been that the behaviour of the fishermen
has magnified the signal (the change in size-composition) in the
stock produced by the change in the amount of fishing. Thus the
size-composition in the landings has become more sensitive to the effect
of fishing, though it may provide a biased estimate of the extent of
the effect.

Care should be used in interpreting the signal, especially in
stocks that may be subject to natural variations in recruitment, and
when observations extend over only a short period. Garcia and Josse
(1988) point out that in such fisheries, when the most recent
recruitment has been poor, fishing may be concentrated on the older
fish (the survivors of earlier good recruitment) and the
length-frequency will include many large fish, and indicate low mortality,
and a healthy fishery. Conversely, if recent recruitment is good,
fishing will concentrate on small fish, and the length-frequency will
suggest high mortality and a fishery in a poor condition. The result
is length-frequencies during the increasing and decreasing phases of
an oscillating fishery that are very like those of heavy and lightly
fished stocks (see Figure 4.3, and compare it with Figures 4.1 and
4.2). As Garcia and Josse point out, few fisheries are in equilibrium
and a single snapshot, whether of age- or length-composition or any
other characteristic of the fishery, is not necessarily an indication
of equilibrium conditions. In practice it should be easy on the basis
of the history of the fishery (trends in catch, and in available
indices of fishing activity - sophisticated measures of fishing
effort are not necessary for this purpose) to determine whether the
difference in the two length-compositions reflects the effects of
fishing or of natural fluctuations.

Even a very simple examination of changes in the
length-composition over a period when the amount of fishing is changing can
therefore be very valuable. In these examples the length-data
confirm, in a quite independent way, the impression from the catch
statistics that the stocks had become, at the beginning of each war,
very heavily fished. In the case of hake the length- data also
suggest that that the fishing pressure of hake had, by 1955, reached
a level surpassing that of the inter-war period. The length-data also
indicate that there had been changes in fishing practice involving
a shift away from small fish. These may not be assessments in the
quantitative sense, but they are still valuable conclusions in
themselves, and in pointing the way for quantitative assessments.

Figure 4.3 The danger of shot assessments in a fluctuating
fishery. Note the difference in catch-curves (middle
figures) taken at different points in the cycle (from
Garcia and Josse, 1988)

A simple measure for monitoring the stocks, in the absence of
more detailed analysis, is provided by the mean length of fish in the
catch. An early example is that of Henderson (1972), who examined
data for a trout fishery in Colombia (Figure 4.4). During the nearly
twenty years of data there was a steady decrease in mean length,
possible with two periods of relatively little change, as indicated
by broken lines. This strongly suggests increasingly heavy fishing,
and this is a conclusion that could not have been obtained from other
available sources. Examination of mean length (based on regular
samples, even if they are not large) should be done to monitor the
“health” of all fisheries, even when there is no time, or resources,
to set up a proper stock assessment programme.

A long-term assessment, aimed at producing advice on the average
steady-state relations between the amount and selectivity of fishing
and the catches, will be based on one or other of the standard
families of models (production models, or dynamic pool models).
Length-data (like age-data) are not normally of direct use in
applying production models, but there are exceptions. Csirke and
Caddy (1983) noted that the standard relation between fishing effort
and long-term catch could be rewritten to relate catch to total
mortality. That is, from the relation

C = af + bf2

(4.1)

where C = catch, f = effort and a and b are constants,
and writing Z = F+M, and F = qf, we have

C = (a/q) (Z-M) + (b/q2) (Z-M)2,

(4.2)

Thus, if the catch in any period is plotted against the
estimated total mortality in that period the result should be a
parabola, similar to that obtained from the more usual plot of catch
against fishing effort, but displaced to one side so that it cuts the
x-axis where Z = M, as well as at some high value of Z. This approach
can be applied to any set of length-data from which values of Z/K
have been obtained by any of the methods described earlier.

This is a deceptively attractive method, but there are problems.
Practical experience of those stocks in which effort has varied over
a wide range suggests that the relation between catch and effort is
seldom a parabola, but descends more gradually at high levels of
effort. The relation, whether parabolic or otherwise, only holds for
stocks in equilibrium, so that the method can strictly only be
applied to a number of periods during each of which the fishing
effort has remained constant, whereas on most stocks fishing effort
is changing continuously. If it has been increasing, the catch in the
current year is likely to be higher than it would be in a steady
state with the current level of effort. The latter problem may be in
part balanced by the fact that the mortality rate estimated from the
length-data in say 1987, is likely to measure the mean mortality over
the last few years, rather than in 1987, but the balance is unlikely
to be exact. The same problem occurs in the normal method of applying
the production model, but various methods, from Gulland's (1961)
method of considering average effort over some earlier period,
onwards have been developed to deal with this.

Figure 4.4 Changes in mean weight in the Colombian trout fishery as an index of the intensity
of fishing (from Henderson, 1972)

The greatest difficulty in applying Csirke and Caddy's method
is likely to be in fitting the theoretical curve to a set of
observations. Fitting a parabola or any strongly non-linear relation
is always difficult, and the statistical problems are increased by
the fact that there is likely to be considerable error in the
independent variable (Z/K), as well as natural variation in the
catch. It is always worthwhile looking at alternative methods of
assessment, but in this case the results should be treated with
considerable caution unless the plot of catch against Z/K gives a
very clear relation.

Length data are well suited to use in many forms of the dynamic
pool models. The commonest formulation of the dynamic pool model is
that of Beverton and Holt (1957). In its simplest form this assumes
recruitment is constant, or is independent of adult stock, and the
assessment is concerned with seeing how the yield-per-recruit (Y/R)
varies with the amount of fishing and the size at the first capture.
Their expression for yield-per-recruit can be rewritten in the
following simplified form (Beverton and Holt, 1964);

Y/R = aE (1 - c)M/K X Sum{Un(1 - c)n/[1 + n(K/M) (1 - E)]}

(4.3)

where E is the exploitation rate F/Z

a is a constant

c is the relative size at first capture 1c/Linf

n is a dummy variable, the summation being over the values
0 - 3

and Un takes values of +1, -3, +3 and -1 for the n values between 0
and 3.

This expression makes it clear that the basic relations between
Y/R and the amount of fishing or the size at first capture depend
only on three ratios. One, M/K is characteristic of the fish stock,
and the others E (=F/Z) and c (=1c/Linf) are determined by the
intensity of fishing and the size of first capture. Since c relates
directly to length, and most of the length-based methods of
estimating mortality give the results in terms of ratios such as Z/K,
it is seen that this formulation can be used almost immediately once
the parameters of growth and mortality have been estimated as in
section 3.

Apart from expressing the yield-per-recruit as a function of
simple ratios, the revised Beverton and Holt formulation also makes
it clear that the variety of Y/R relationships (given the assumption
that fishing mortality is constant above some selection point) is not
large. In fact there is a single family of relations, depending on
the value of M/K, and for each member of the family there is a
two-dimensional surface relating Y/R to the amount of fishing and to
the size of first capture. The usual Y/R curves are then slices
through this surface. Calculating a Y/R curve (or surface) involves
nothing new, and should now be a matter of applying a simple computer
programme, which can be done on spreadsheets (Gulland and Gibson, in
press) or just by looking up the table in Beverton and Holt (1964)
for the appropriate value of M/K. It should not in itself be
considered as carrying out an assessment.

The simplest type of stock assessment, in the context of Y/R
curves, consists of two phases: identifying the curve (or surface)
corresponding to the biological characteristics of the stock, and
locating the present position of the fishery on this curve. In both
of these the estimation of M (or M/K), or the division of the total
mortality between fishing and natural mortality is an important step
and one that usually presents the biggest problem. If one has been
lucky to start investigations on an unexploited stock then in that
stock M = Z and any of the methods of the previous section to
estimate Z (or Z/K) will produce an estimate of M (or M/K). Once a
fishery starts, then mortality will increase, and the amount of the
increase in Z/K will provide an estimate of F/K. This points to the
advantages of studies carried out before fishing begins.

More usually studies do not begin until a fishery is well
established. In these cases most of these methods will produce
estimates of Z (or Z/K). There are then several ways of proceeding:

separating F and M by relating changes in Z to changes in the
amount of fishing;

estimating F directly, e.g., by tagging, or from the ratio of
catch to the biomass as estimated by some kind of survey;

estimating M directly e.g from the consumption by predators.
This method is at best approximate, and likely to provide a
lower bound, but some recent studies in the North Sea (ICES
1989) show that this method can provide interesting results.

estimating M by comparison with the values of M in other
species.

The first method is the one that is most likely to give
statistically sound results, and should be used when possible. Its
typical age-based form consists of regressing Z on the fishing effort
f. Exactly the same procedure can be used with length-based
estimates, either of Z, or as occurs with some methods, of Z/K. In
the latter case we obtain estimates of M/K and F/K.

Even when it is not possible to apply the regression method
exactly for some reason, e.g., because there is no exact measure of
effort, an examination of less quantitative material can provide
guidance on the relative values of F and M. Thus Gulland (1956) used
the slope of the lines in Figure 4.1 as indices of Z. By noting that
the fishing effort during the war was around one third of the pre-war
level, he estimated that in the pre-war period fishing accounted for
at least half the total mortality. Even in situations where the data
are still less quantitative some approach of this kind should be
made. Formal effort data may be completely lacking, but some idea of
how the amount of fishing has been changing can usually be obtained
from records of one kind or another - What is the impression of local
fishermen? Have new markets opened up? In many cases these records
will indicate that there have been changes in the amount of fishing,
and then one needs to see whether there are any changes in the stock
that might give some measure of the impact of fishing. Are large fish
less frequent than they used to be? Have catch rates declined? If
these signs have occurred, then it is reasonable to suppose that
fishing is having an impact and that F is now a non- negligible
proportion of Z. If they have not, F is probably still small.

A length-based version of examining the effects of fishing on
the composition of the population, that does not require any direct
estimate of fishing effort (or cpue), but relies on accurate
statistics of total catch as an index of the amount of fishing, has
been developed for sperm whales (Beddington and Cooke, 1981; Cooke
and Beddington, 1982). The greater the change in length-composition
that is observed following a catch of a given magnitude, the lower
must have been the initial population and the higher the fishing
mortality. The method requires that the total numbers caught in each
length-group are known, and assumes either that the selection pattern
of the fishery as a whole is constant, or that the catch data for
each year can be broken down into small time/area strata, within each
of which selection is the same from year to year. Alternative initial
values of population numbers and growth parameters can be used to
project the population forwards, and the set of parameter determined
that give the best fit between observed and projected catches by
length-group. The data requirements and assumptions about constant
selectivity are rather stringent. Thus, although the method is
equally applicable in principle to any fish stock in which there is
appreciable post-recruitment growth, in practice its application to
finfish is likely to be limited. Further details of the method are
given in the International Whaling Commission reports, and a FORTRAN
version of the program is available from the authors and from the
IWC.

The second method, of estimating F as the ratio of catch to
biomass does not formally involve length, and does not need
discussion in this manual. However, it is worth noting that it is
unlikely that the biomass, as measured by the survey gear, is
precisely the same biomass as exploited by the fishery. Generally the
survey will include smaller fish (for example, a trawl survey is
usually done with a small mesh in order to collect information on
pre-recruits and on small unexploited species). In that case the
survey biomass should be adjusted downward to cover only the
exploited part of the stock. This will be most easily done on the
basis of length. If recruitment to the exploited stock is fairly
abrupt, at some length lc, then all fish smaller than lc should be
omitted from the survey data, and the biomass recalculated
accordingly. If selection occurs over a wide range of sizes a value
of lc may be difficult to determine. Then it may better to take some
arbitrary value of lc above the selection range and calculate the
weight of catch and stock above lc.

The third method, of directly estimating that part of M
accounted for by predation is likely to be of value in fisheries with
large research programmes, but is possibly of limited immediate
relevance to many users of this manual. However, it is worth pointing
out here that, because predation rates are largely determined by the
relative sizes of predator and prey, a length-based approach to this
method is likely to be fruitful. Pope and Yang (1987) describe how
this may be done, using a multi-species extension to Jones' (1984)
length cohort analysis. It is also worth noting here that this
approach is providing much new insight into how natural mortality is
determined. The North Sea results show that the predation mortality
among the smaller sizes of fish is much greater than the values of
natural mortality previously used for those species, and that M for
a given species almost certainly can decrease quite substantially
with size. To the extent that the abundance of the predator
populations can vary from year to year, due for example to the impact
of fishing, it is probable that natural mortality also changes, as
suggested by Munro (1982) and others. Though such changes do not seem
to have been clearly demonstrated, principally due to the problems
of obtaining two good estimates of M, this is no reason for not
believing that they can occur. To the extent that these changes with
size and time occur it may be misleading to talk about “the natural
mortality of mackerel” in a particular area as though it was a unique
and unvarying quantity.

In practice none of the first three methods may give usable
numbers for M (or F, in the common case when Z can be estimated). If
a long-term assessment is to be presented, some assumption about M,
or M/K, has to be made if the dynamic pool approach is to be
followed. It is natural in such cases to fall back on the comparative
method. The commonest form to use is Pauly's (1980), which has been
used so often in length based studies (e.g., in the ELEFAN packages)
that it is sometimes thought of as a length-based method, which it
is not. Pauly's equation is

logM = -0.007 - 0.279 logLinf + 0.654 logK + 0.463 logT

(4.4)

where T is the mean environmental temperature Celsius. This formula
has potentially a great advantage in that confidence limits on the
estimate are available. The regression on which this equation is
based has a residual standard deviation about the regression of
0.245, or transforming from logarithms (these are to the base 10),
the width of the approximate 95% confidence limits of 2.5 times the
central estimate (i.e., if the estimate is 0.2 the confidence
interval is approximately 0.07-0.57) about the central estimate given
by equation 4.1. These are wide limits, so it is perhaps not
surprising that they are rarely if ever used. It may be argued that
they may be too wide, since they take into account the undoubted
uncertainty in the estimates used by Pauly as well as the true
variability from stock to stock. On the other hand the uncertainties
in K, Linf and T for the stock being studied (which may be large) are
not taken into account. They would make the true confidence limits
for the estimates of M wider than given here. The degree of
variability can often be reduced by considering only closely related
species (e.g., clupeoids) since there is good evidence (Beverton and
Holt, 1959; Beverton, 1963) that there are greater similarities in
population parameters within groups of fishes than among fishes as
a whole. Against this it can be argued that many of the estimates of
mortality used by Pauly were published after the general pattern of
values of M were known and authors tended, when their estimates were
poor, only to publish those that fitted expectations.

Whatever the truth of these arguments it is clear that any
figure for M produced from Pauly's equation must be subject to
considerable uncertainty. Even if the standard deviations presented
by Pauly may be too wide, the failure to take explicit account of
substantial uncertainty is likely to be misleading. Possible
confidence limits which reflect the likely spread might be ones
extending half as far above the central estimate as the confidence
limits suggested above. Then, if the central estimate of M from
equation 4.4 is M = 0.36, our conclusion should be that the true
value of M is somewhere between 0.21 and 0.61, and these values
should be used as alternatives in the further assessments. In some
circumstances, for example if our estimate of Z is 1.55, the range
is narrow enough to show that the stock is heavily fished (M is at
most just less than half Z), but more often the status of the stock
will remain unclear. It was perhaps optimistic of Pauly (1987, p. 23)
to claim that, when using ELEFAN II (which includes this method of
estimating M), “it is in principle possible to assess whether or not
a stock is over-fished, based solely on length frequency data
obtained from that stock” - though the point is not so much that this
is an unrealistic belief in the power of length-based methods, but
that any method has difficulty in assessing the state of a stock
unless there are observations of the stock and its size- or
age-composition under different intensities of fishing.

The point is that, when there is uncertainty about the value of
a parameter, subsequent computations should be done using a range of
values applies to any parameter. It is stressed here because the
uncertainties about M (or M/K or the ratio E = F/Z), whether based
on Pauly's equation or other methods, are usually much greater than
in other parameters.

Though length methods are considered an innovation in much
assessment work, they have a long history of use in estimating the
effect of selection changes, particularly in the North Atlantic
(Gulland, 1961a; 1964). The principle used is simple; from the change
in selectivity and the length-composition of the current catches the
immediate change in the numbers caught following a change in
selectivity can be calculated. In the long run, catches will increase
when the fish released have grown enough to be caught by the new
gear. There are two ways of estimating this increase; the original
method of Gulland, which computes this increase in the numbers caught
as the product of the numbers released times the exploitation ratio
(F/Z), reduced by the natural mortality prior to the time when they
are big enough to be retained by the larger mesh; and the method of
Cadima (1978) which computes the change in fishing mortality.

The basic calculations are set out in Table 4.1, derived from the
haddock data given by Gulland (1983). For each length group the
number retained can be calculated as nk=n1p2/p1 where p1 and p2 are the
proportion retained by the original and new gear respectively, as
determined by selection experiments where n1 = numbers in the
original catch, and nk = numbers retained with the new gear
immediately after the change. The total numbers N and weight W caught
before and immediately the change can then be calculated as the sums
of n1, n1wL nk and nkwL.

Table 4.1 Basic calculations of the effect of an increase in mesh size

Length

Meanweight

% retained

Ratio

Numbers of fish

90 mm

120 mm

Initial

Retained

Released

w1

p1

p2

n1

nk

nR

25

160

50

3

.06

8

0.48

7.52

30

260

80

16

.2

314

62.8

231.2

35

420

98

100

.42

1084

435.5

630.5

40

630

100

100

.72

1409

1014.5

394.5

45

880

100

100

.94

1370

1287.8

82.2

50

1190

100

100

1

952

952

0

55

1570

100

100

1

465

465

0

60

1760

100

100

1

255

255

0

65

2530

100

100

1

124

124

0

70

3100

100

100

1

73

73

0

75

3800

100

100

1

30

30

0

80

4600

100

100

1

9

9

0

Total numbers

6093

4727

1365

Total weight

5639

4986

652

% of initial numbers

77.6

22.4

% of initial weight

88.4

11.6

From the table the immediate effect of the change is given as
the ratio of the weight released to initial weight i.e. WR/W1 =
652/5639 = 11.6%. Using Gulland's approach, in the long run an
additional number of fish, ENR, will be caught, where NR' =
NRexp(-Mdt) where dt is the time taken by the fish to grow from the
mean selection length of the two gears. The catches will then
increase by a factor A = Nk/Nr'. The long term weight W2 is given by
W2 = Wk (1 + A). Using Cadima's method the long term weight W2 is
given by W2 = Wkexp(Fdt), and exp(Fdt) can be shown to be equal to
(N1/Nk), where E' is the value of E = F/Z in the size range between
the selection sizes of the two gears.

The method can be expanded to give the interim effects during
the period between the change and the time when the new long-term
equilibrium is reached (Gulland 1964). To do this we note that, if
all fish grow at the same rate, then at any given time in the
transition period, the older and larger fish (above length 1" say)
will be unaffected by the change while the fish smaller than 1" will
have reached the new equilibrium. The weight caught W" will then be
given by

W" = WK,L + W1,L (1 + A) = Sum [WK,L (1+A)]

1>1" 1>1"

Like many length-based methods this method makes the assumption
that the fishery is in equilibrium. Its particular advantage is that
it can deal with a situation in which several gears exploit the same
stock (e.g., trawlers and longliners), some of which may not alter
their selectivity. In this case the values of N1, Nk, W1 and Wk are
calculated for each gear separately. The long-term effects and the
immediate effects can then be compiled after calculating NR as the
sum of all the values of iNr for the individual gears.

Jones (1984) has pointed out that the procedures of cohort
analysis (see section 3.2.4) can be extended to provide estimates of
the changes in long-term catch as a result of changes in fishing
mortality. For any length-group the numbers present in the new
equilibrium state, 2Nl, can expressed as

2NL = 1NL × CF

where CF is a correction factor due to changed mortalities, given by
CF = exp[sum(1Fdt) - sum(2Fdt)] and 1Nl are the numbers present in the
original state, 1F and 2F are the original and new fishing
mortalities, dt is the time taken to grow through the length
interval, and the summations are taken from the recruitment size up
to the middle of the lth length interval.

The new catches in each length interval, expressed as weight or
numbers, will then be given as

2CL = 1CL × CF × 2FL/1FL
and
2WL = 1WL × CF × 2FL/1FL.

It can be seen that there need be no assumption of F being the
same for all age groups. It is thus possible to use the method for
simultaneous changes in the amount of fishing and in selection. An
example of this is given in Table 4.2 (taken from Table 7 of Jones,
1984). The caution to be noted in using the procedures in this table
is that the summations of F (columns 7 and 8) are taken to the middle
of each length-group, while most of the calculations in VPA and
cohort analysis are to the boundaries of the groups.

The approach set out in Table 4.2 follows directly from Jones
original form of length-based cohort analysis set out in Table 3.5.
It is of course possible to use the cohort slicing approach as in
Table 3.6. In that approach, once the slicing is done, then the
individual slices can be treated as age-groups (actually half-year
groups in Table 3.6, because the fish were short-lived). In that case
the data can be analysed using standard age-based techniques, with
the proviso that the results will become progressively less reliable
among the larger fish as there is blurring of age-groups across
slices.

Sparre et al. (1989, chapter 5) have suggested a very similar
set of calculations, starting with the approach of Thompson and Bell
(1934). It can be viewed as the reverse of cohort analysis (or VPA)
in that instead of working back from the observed catches from a
cohort to deduce the fishing mortality, it works forward from the
numbers of a cohort recruiting to the fishery, to deduce (given the
mortality in each length-interval) the numbers caught, and also the
weights. An advantage of this method is that it incorporates
information on the value of the catch. This can be important for
those fisheries (e.g., on shrimp) where the price per kilogramme
differs according to the size of the animal.

Most of the assessment techniques discussed so far deal with
steady-state conditions, and thus provide long-term strategic advice.
Is it desirable to increase fishing effort by building new boats? Is
the stock so heavily fished that measures to manage the fishery are
necessary? What would be the long-term effect of increasing the mesh
size by 10 mm? This is probably the most valuable type of advice, but
increasingly, especially when management is being considered,
short-term advice is needed. What is the immediate effect of using a bigger
mesh? How long after reducing fishing effort on a heavily fished
stock will it be before catches return to their original level (or
better)? This type of advice has become particularly important in the
parts of the North Atlantic and other areas where the amount of
fishing is controlled by catch quotas or TACs.

Though some of the techniques described above, e.g., Gulland's
mesh change method, can provide information on short-term interim
effects, most of the length-based techniques deal with steady states,
and age-based methods are usually better (because they have a simple
time-scale) for studying short term effects. There may be exceptions.

One possible exception is the prediction of future catches in
setting TACs. The stocks concerned are mostly assessed by cohort
analysis or VPA. Future stock sizes and catches (in numbers) can be
predicted by projecting the matrix of numbers at age forward one
year. The total weight caught can then be estimated by multiplying
the numbers by the average weight-at-age. This procedure is fine
provided the average weights do not change. In practice there are
often secular changes in mean weight which can sometimes lead to
serious errors in predicting TACs.

Shepherd (1987) has pointed out that essentially the same
technique can be used on length-data, though the projection is more
complex. For age-data

Ni+1,j+1 = Ni,je-z

where Ni,j are the numbers at age j in year i

For length-data the projection is more complicated, since it is
unlikely, even if all fish follow exactly the same growth pattern,
that all the fish in one length-group in one year will all fall in
a single length group in the next year. For example fish between 60
and 65 cm in one year may be between 67.5 and 71.7 cm in the next
year, and thus are divided between two different 5-cm groups.
Nevertheless, by considering the sizes, in the second year, of fish
initially at the boundaries between adjacent length-groups (e.g., 10,
15, 20 cm, etc.) in the first year, and applying the expected
mortality rate, it is possible to calculate expressions for the
expected frequencies in each length-group in the second year, as a
function of the first-year frequencies. The exceptions are the
smallest sizes, which are occupied by recruits. To the extent that
departures in the mean weights-at-age in the second year from the
expected values are due to unusual growth in the earlier years,
rather during the transition period, this approach should be less
disrupted than the age-based approach.

So far this method has not been tested sufficiently to be sure
that this is the case. Shepherd (1987) has applied the approach to
data from surveys of cod in the North Sea. The results were
promising, though the predictions were not very accurate, possibly
because there was a lot of variability in the original data. Another
possible advantage of the method is that, because the input data are
simple, and there is no work involved in processing and reading
otoliths and scales, there can be a shorter lead-time between making
the observations and producing the predictions. This in itself could
lead to greater precision. For the present though not enough has been
done to apply the method in practice to be able to recommend it.

One big difference between age-data and length-data is that the
latter can be collected in a much greater volume, and large numbers
of different length samples of meaningful size (say 200 fish plus)
can be collected from different places and times. In contrast the
practical constraints of manpower mean that few age samples of
comparable size can be collected. For age-data therefore we are
usually constrained to look at pooled data, for the fishery as a
whole during a month or even a year. For most of the methods
described in this report this difference does not matter - most of
the methods use pooled data. However, the act of pooling does throw
away information that could be of use for other purposes.

One obvious use of detailed information on length composition
in management is to identify those areas, times or gears in which
small fish are unusually abundant. Closing fishing on nursery
grounds, or at times when small fish are recruiting, or discouraging
fishing by gears that take predominantly small fish is often the best
way of improving the exploitation pattern, i.e., moving the effective
size at first capture upwards and thus increasing the
yield-per-recruit. This identification can be done in many ways. Any
differences between fishing grounds are probably seen by plotting the
mean length of each sample at the position of capture on a chart of
the fishing grounds.

Looking at individual samples can also help in the interpretation
of many of the techniques described earlier. For example in Figure
3.3a (p. 26) the length distribution for September clearly does not
fit the predicted growth-curve. It would be helpful to know if this
was a single sample, and if the fish were caught in the same area as
the other samples. It would probably also be helpful to know whether
the large number of fish in January (1 390) came from several samples
with the same length distribution, or whether the observed broad
distribution arises from the combination of several samples with
different modal lengths.

It is not the purpose here to set out recommended ways to
proceed with detailed length composition data. The point to be made
is that these data probably contain much useful information and
looking at and arranging the data in different ways is part of the
essential process of understanding the data which should precede any
application of the process of understanding the data which should precede any
detailed data can be quite simple, but equally sophisticated methods
can, and should, be used when appropriate. Thus McGlade and Smith
(1983) applied principal component analysis to length data of
Canadian commercial landings of pollock to provide insight into the
patterns of movement and distribution of this species.